Question

find the exact value:
tan40/cot50

sec55/csc35

SHOW ALL WORK!

Answer 1

I don't know what you mean by exact value but http://puu.sh/qaNl

Answer 2

HELP!

Answer 3

the answer to this problem is 1 but i dont know how to do it

Answer 4

@amistre64

Answer 5

Wait, is it (tan40/cot50) * (sec55/csc35) or two separate questions?

Answer 6

two separate problems

Answer 7

??????

Answer 8

\[\tan(40)=\sin(40)/\cos(40)\]Similarly:\[\cot(50)=\cos(50)/\sin(50)\]This implies:\[\tan(40)/\cot(50)=(\sin(50)\sin(40)) \div (\cos(50)\cos(40))\]By a product rule for trigonometric functions (which can be viewed at http://www.proofwiki.org/wiki/Product-to-Sum_Formulas_for_Sine_and_Cosine), we obtain:
\[(\cos(50-40) + \cos (40+50))/2 \div (\cos(50-40)-\cos(50+40))/2\]Here it is fairly easy to see that since the numerator and denominator are equal, the final quotient will be 1. These questions are often just a matter of finding the correct trigonometric formula or technique to employ.

Answer 9

your very helpful! But can u tell me EXACTLY HOW you got this: (cos(50−40)+cos(40+50))/2÷(cos(50−40)−cos(50+40))/2

Answer 10

There's a simpler solution: Notice that tan(x)=cot(90-x) for x in degrees. So cot(50)=cot(90-40)=tan(40). Therefore, tan(40)/tan(40)=1.
For sec(55)/csc(35), we use sec(x)=csc(90-x). Since csc(35)=csc(90-55)=sec(55), this is also equal to 1.